The drying times of a certain type of new paint are known to follow normal distribution with mean µ == 75 mins and standard deviation o = 9 mins. Chemists have proposed a net additive to shorten the drying time. It is believed that with this new addition, the dryin, times are still normally distributed with the same variance but with a smaller mean parameter H. One is therefore interested in testing Ho u = 75 versus H : u < 75. Experts in the area decide that a value for u smaller than 70 indicates a practically useful improvement, therefore a rejection region for Ho in favor of H is taken to be {X < 70}, where X is the sample mean based on a random sample of size n from the paint with this new addition. (a) Calculate and interpret the probability of type 1 error. (b) Calculate and interpret the probability of type 2 error when the true u = 68. (c) What's the smallest sample size n such that this test procedure (reject Ho when X < 70) has only 10% probability of type 2 error when the true u = 68? (d) Determine the test procedure that has a fixed probability of type 1 error equal to a ..izo

The drying times of a certain type of new paint are known to follow normal distribution with mean µ == 75 mins and standard deviation o = 9 mins. Chemists have proposed a net additive to shorten the drying time. It is believed that with this new addition, the dryin, times are still normally distributed with the same variance but with a smaller mean parameter H. One is therefore interested in testing Ho u = 75 versus H : u < 75. Experts in the area decide that a value for u smaller than 70 indicates a practically useful improvement, therefore a rejection region for Ho in favor of H is taken to be {X < 70}, where X is the sample mean based on a random sample of size n from the paint with this new addition. (a) Calculate and interpret the probability of type 1 error. (b) Calculate and interpret the probability of type 2 error when the true u = 68. (c) What's the smallest sample size n such that this test procedure (reject Ho when X < 70) has only 10% probability of type 2 error when the true u = 68? (d) Determine the test procedure that has a fixed probability of type 1 error equal to a ..izo

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The mean ±1 sd of ln [calcium intake (mg)] among 25 females, 12 to 14 years of age, below the poverty level is 6.56 ± 0.64. Similarly, the mean ± 1 sd of ln [calcium intake (mg)] among 40 females, 12 to 14 years of age, above the poverty level is 6.80 ± 0.76. 8.2 Test for a significant difference between the variances of the two groups. Find the P value. Do not use excell. Solve the step by step
The time it takes for a compact fluorescent bulb to reach full brightness is normally distributed with mean 29.9 seconds and standard deviation 4.1 seconds. Find and interpret the z-score for x = 26.4.
At the alpha = 0.01 level , what is the correct conclusion for this test? The daily temperatures in fall and winter months in Virginia have a mean of 62F. A meteorologist in southwest Virginia believes the mean temperature is colder in this area. The meteorologist takes a random sample of 30 daily temperatures from the fall and winter months over the last five years in southwest Virginia. The mean temperature for the sample is 59 degrees * F with a standard deviation of 6.21 degrees * F The meteorologist conducts a one -sample t-test for and calculates a P value of 0.007. The meteorologist should reject the null hypothesis since 0.007 < 0.01 . There is convincing evidence that the mean temperature in fall and winter months in southwest Virginia is less than 62 F. The meteorologist should reject the null hypothesis since 0.007 < 0.01 . There is not convincing evidence that the mean temperature in fall and winter months in southwest Virginia is less than 62 F. The meteorologist…
(3) A process for manufacturing soft soda produces normally distributed yield with a mean of 600 and a standard deviation of 100 units. A new modified process yields an average of 630 units for a sample of size 50. At a = 0.05 does the modified process increase the yield? %3D
number 28 The following data shows the price of a certain stock over the last 8 months. Month Price 1 2.10 2 1.98 3 2.01 4 1.89 5 1.90 6 1.89 7 1.72 8 1.65 (a) Develop a scatter diagram and draw a trend line through the points. A graph has a horizontal axis labeled "Month" with values from 0 to 10 and a vertical axis labeled "Price" with values from 0 to 2.5. The scatter diagram has 8 points. A line goes through the center of the pattern of points. A pattern goes down and right becoming more steep from (1, 1.7) to (8, 1.25). A graph has a horizontal axis labeled "Month" with values from 0 to 10 and a vertical axis labeled "Price" with values from 0 to 2.5. The scatter diagram has 8 points. A line goes through the center of the pattern of points. A pattern goes down and right from (1, 2.1) to (8, 1.65). A graph has a horizontal axis labeled "Month" with values from 0 to 10 and a vertical axis labeled "Price" with values from 0 to 2.5. The scatter…
The mean life expectancy in the US pop. is currently 81.1 years with a standard deviation of 15.9. A researcher examined the age of death of 70 people in Florida hospitals and the mean was 85.2 yrs. He runs a 2tailed test with a=.05 to see if FL has significantly different life expectancy to the overall US pop. Calculate the standard error, z statistic and critical z values from this information.
Currently patrons at the library speak at an average of 61 decibels. Will this average increase after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 57 people speaking at the library. Their average decibel level was 63.8 and their standard deviation was 9. What can be concluded at the the αα = 0.10 level of significance?
A sample of 50 earthquakes was found to have a sample mean of x ¯ = 1.184 and a sample standard deviation of s = 0.5864. Test the claim that the population of earthquakes has a mean magnitude greater than 1.00. Use a 0.01 significance level. Find the test statistic and critical value used for this test. Round to three decimal places.
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 260 engines and the mean pressure was 4 lbs/square inch. Assume the variance is known to be 0.64. If the valve was designed to produce a mean pressure of 4.1 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.
0.6.3 Question 3 Is the cubic effect significant? How about quadratic and linear effects? Analysis of Variance Table Response: EX Df Sum Sq Mean Sq F value Pr(>F) MET 1 332 332 0.1246 0.7257742 I(MET^2) 1 37504 37504 14.0572 0.0005141 *** I(MET^3) 1 7245 7245 2.7154 0.1065086 Residuals 44 117390 2668 > anova(quadModel) Analysis of Variance Table Response: EX Df Sum Sq Mean Sq F value Pr(>F) MET 1 332 332 0.120 0.7306134 I(MET^2) 1 37504 37504 13.541 0.0006216 *** Residuals 45 124635 2770 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The braking ability was compared for two car models. Random samples of two cars were selected. The first random sample of size 64 cars yield a mean of 36 and a standard deviation of 8. The second sample of size 64 yield a sample mean of 33 and a standard deviation of 8. Do the data provide sufficient evidence to indicate a difference between the mean stopping distances for the two models? Use Alpha= 0.01. Ho: µ1 – µ2 = 0 vs. Ha: µ1 – µ2 + 0 .p-value = 0.0017. Reject Ho Но: Д, — м2 — 0 vs. Ha:M1 — M2 + 0. p-value — 0.034. Ассеpt Ho O Ho:µ1 – Hz Но: И — 2 — 0 vs. Ha:M, — нz + 0. p-value —D 0.0017. Ассept Ho Ho: H1 – U2 = 0 vs. Ha: µ1 – µ2 + 0. p-value = 0.034. Reject Ho
Kindly answer this engineering data analysis problem